"You just don't do this. I have a lot of threats on my life. It's incitement. I'm going to the police – I want them to know that a law's been broken."

She added that she regarded Compton's remarks as racially motivated because he mentioned stoning.

"If I as a Muslim woman had tweeted that it would be a blessing if Gareth Compton was stoned to death I'd be arrested immediately. I don't think the nasty Tories went away."

Compton, the Conservative councillor for Erdington, said he was writing in response to comments made by Alibhai-Brown on Radio 5 Live.

The councillor claimed she had said, with reference to David Cameron's trip to China, that no politician was morally qualified to speak out about human rights abuses, including the stoning of women, bar the likes of Nelson Mandela.

Compton, who later apologised on Twitter, added: "Twitter is a forum for glib comment of the moment. It was a glib comment. Who could possibly think it was serious?

"Obviously I apologise. No offence was intended."

The incident would not be the first time that a politician has been landed in hot water as a result of comments posted on Twitter.

A Labour candidate was sacked during the general election campaign after posting a series of offensive comments about other politicians, voters and celebrities on his Twitter page.

Stuart MacLennan, who was standing in the Moray constituency in Scotland, described the elderly as "coffin-dodgers" in one comment and complained about being "up north again in his constituency".

• This article was amended on 11 November 2010. The online headline referred to Gareth Compton as an MP. This has been corrected.